Thermoelastic dissipation in MEMS/NEMS flexural mode resonators.

Understanding the energy dissipation mechanisms in single-crystal silicon MEMS/NEMS resonators are particularly important to maximizing an important figure of merit relevant for miniature sensor and signal processing applications: the Quality factor (Q) of resonance. This paper discusses thermoelastic dissipation (TED) as the dominant internal-friction mechanism in flexural mode MEMS/NEMS resonators. Criteria for optimizing the geometrical design of flexural mode MEMS/NEMS resonators are theoretically established with a view towards minimizing the TED for single-crystal silicon MEMS/NEMS flexural mode resonators.

Probabilistic fault identification using vibration data and neural networks

Bayesian formulated neural networks are implemented using hybrid Monte Carlo method for probabilistic fault identification in cylindrical shells. Each of the 20 nominally identical cylindrical shells is divided into three substructures. Holes of (12±2) mm in diameter are introduced in each of the substructures and vibration data are measured. Modal properties and the Coordinate Modal Assurance Criterion (COMAC) are utilized to train the two modal-property-neural-networks. These COMAC are calculated by taking the natural-frequency-vector to be an additional mode. Modal energies are calculated by determining the integrals of the real and imaginary components of the frequency response functions over bandwidths of 12% of the natural frequencies. The modal energies and the Coordinate Modal Energy Assurance Criterion (COMEAC) are used to train the two frequency-response-function-neural-networks. The averages of the two sets of trained-networks (COMAC and COMEAC as well as modal properties and modal energies) form two committees of networks. The COMEAC and the COMAC are found to be better identification data than using modal properties and modal energies directly. The committee approach is observed to give lower standard deviations than the individual methods. The main advantage of the Bayesian formulation is that it gives identities of damage and their respective confidence intervals.

Feasibility of damage detection using vibration data in a population of cylinders

The feasibility of vibration data to identify damage in a population of cylindrical shells is assessed. Vibration data from a population of cylinders were measured and modal analysis was employed to obtain natural frequencies and mode shapes. The mode shapes were transformed into the Coordinate Modal Assurance Criterion (COMAC). The natural frequencies and the COMAC before and after damage for a population of structures show that modal analysis is a viable route to damage identification in a population of nominally identical cylinders. Modal energies, which are defined as the integrals of the real and imaginary components of the frequency response functions over various frequency ranges, were extracted and transformed into the Coordinate Modal Energy Assurance Criterion (COMEAC). The COMEAC before and after damage show that using modal energies is a viable approach to damage identification in a population of cylinders.

Optimisation of a piezoelectric system for energy harvesting from traffic vibrations

Piezoelectric systems are viewed as a promising approach to energy harvesting from environmental vibrations. The energy harvested from real vibration sources is usually difficult to estimate analytically. Therefore, it is hard to optimise the associated energy harvesting system. This work investigates the optimisation of a piezoelectric cantilever system using a genetic algorithm based approach with numerical simulations. The genetic algorithm globally considers the effects of each parameter to produce an optimal frequency response to scavenge more energy from the real vibrations while the conventional sinusoidal based method can only optimise the resistive load for a given resonant frequency. Experimental acceleration data from the vibrations of a vehicle-excited manhole cover demonstrates that the optimised harvester automatically selects the right frequency and also synchronously optimises the damper and the resistive load. This method shows great potential for optimizing the energy harvesting systems with real vibration data. ©2009 IEEE.

Vibration and stress analysis in the presence of structural uncertainty

At medium to high frequencies the dynamic response of a built-up engineering system, such as an automobile, can be sensitive to small random manufacturing imperfections. Ideally the statistics of the system response in the presence of these uncertainties should be computed at the design stage, but in practice this is an extremely difficult task. In this paper a brief review of the methods available for the analysis of systems with uncertainty is presented, and attention is then focused on two particular "non- parametric" methods: statistical energy analysis (SEA), and the hybrid method. The main governing equations are presented, and a number of example applications are considered, ranging from academic benchmark studies to industrial design studies. © 2009 IOP Publishing Ltd.

Energy scattering in weakly non-linear systems.

The Chinese Tam-Tam exhibits non-linear behavior in its vibro-acoustic response. The frequency content of the response during free, unforced vibration smoothly changes, with energy being progressively smeared out over a greater bandwidth with time. This is used as a motivating case for the general study of the phenomenon of energy cascading through weak nonlinearity. Numerical models based upon the Fermi-Pasta-Ulam system of non-linearly coupled oscillators, modified with the addition of damping, have been developed. These were used to study the response of ensembles of systems with randomized natural frequencies. Results from simulations will be presented here. For un-damped systems, individual ensemble members exhibit cyclical energy exchange between linear modes, but the ensemble average displays a steady state. For the ensemble response of damped systems, lightly damped modes can exhibit an effective damping which is higher than predicated by linear theory. The presence of a non-linearity provides a path for energy flow to other modes, increasing the apparent damping spectrum at some frequencies and reducing it at others. The target of this work is a model revealing the governing parameters of a generic system of this type and leading to predictions of the ensemble response.

Moderate energy impact analysis combining phenomenological contact law with localised damage and integral equation method

A computational impact analysis methodology has been developed, based on modal analysis and a local contact force-deflection model. The contact law is based on Hertz contact theory while contact stresses are elastic, defines a modified contact theory to take account of local permanent indentation, and considers elastic recovery during unloading. The model was validated experimentally through impact testing of glass-carbon hybrid braided composite panels. Specimens were mounted in a support frame and the contact force was inferred from the deceleration of the impactor, measured by high-speed photography. A Finite Element analysis of the panel and support frame assembly was performed to compute the modal responses. The new contact model performed well in predicting the peak forces and impact durations for moderate energy impacts (15 J), where contact stresses locally exceed the linear elastic limit and damage may be deemed to have occurred. C-scan measurements revealed substantial damage for impact energies in the range of 30-50 J. For this regime the new model predictions might be improved by characterisation of the contact law hysteresis during the unloading phase, and a modification of the elastic vibration response in line with damage levels acquired during the impact. © 2011 Elsevier Ltd. All rights reserved.

Active control of high-frequency vibration: Optimisation using the hybrid modelling method

This work presents active control of high-frequency vibration using skyhook dampers. The choice of the damper gain and its optimal location is crucial for the effective implementation of active vibration control. In vibration control, certain sensor/actuator locations are preferable for reducing structural vibration while using minimum control effort. In order to perform optimisation on a general built-up structure to control vibration, it is necessary to have a good modelling technique to predict the performance of the controller. The present work exploits the hybrid modelling approach, which combines the finite element method (FEM) and statistical energy analysis (SEA) to provide efficient response predictions at medium to high frequencies. The hybrid method is implemented here for a general network of plates, coupled via springs, to allow study of a variety of generic control design problems. By combining the hybrid method with numerical optimisation using a genetic algorithm, optimal skyhook damper gains and locations are obtained. The optimal controller gain and location found from the hybrid method are compared with results from a deterministic modelling method. Good agreement between the results is observed, whereas results from the hybrid method are found in a significantly reduced amount of time. © 2012 Elsevier Ltd. All rights reserved.

Impact of mode localization on the motional resistance of coupled MEMS resonators

This paper investigates the effect of mode-localization that arises from structural asymmetry induced by manufacturing tolerances in mechanically coupled, electrically transduced Si MEMS resonators. We demonstrate that in the case of such mechanically coupled resonators, the achievable series motional resistance (R x) is dependent not only on the quality factor (Q) but also on the variations in the eigenvector of the chosen mode of vibration induced by mode localization due to manufacturing tolerances during the fabrication process. We study this effect of mode-localization both theoretically and experimentally in two pairs of coupled double-ended tuning fork resonators with different levels of initial structural asymmetry. The measured series R x is minimal when the system is close to perfect symmetry and any deviation from structural symmetry induced by fabrication tolerances leads to a degradation in the effective R x. Mechanical tuning experiments of the stiffness of one of the coupled resonators was also conducted to study variations in R x as a function of structural asymmetry within the system, the results of which demonstrated consistent variations in motional resistance with predictions. © 2012 IEEE.

A general mass law for broadband energy harvesting

It is well known that the power absorbed by a linear oscillator when excited by white noise base acceleration depends only on the mass of the oscillator and the spectral density of the base motion. This places an upper bound on the energy that can be harvested from a linear oscillator under broadband excitation, regardless of the stiffness of the system or the damping factor. It is shown here that the same result applies to any multi-degree-of-freedom nonlinear system that is subjected to white noise base acceleration: for a given spectral density of base motion the total power absorbed is proportional to the total mass of the system. The only restriction to this result is that the internal forces are assumed to be a function of the instantaneous value of the state vector. The result is derived analytically by several different approaches, and numerical results are presented for an example two-degree-of-freedom-system with various combinations of linear and nonlinear damping and stiffness. © 2013 The Author.

Efficient parametric uncertainty analysis within the hybrid Finite Element/Statistical Energy Analysis method

This paper is concerned with the development of efficient algorithms for propagating parametric uncertainty within the context of the hybrid Finite Element/Statistical Energy Analysis (FE/SEA) approach to the analysis of complex vibro-acoustic systems. This approach models the system as a combination of SEA subsystems and FE components; it is assumed that the FE components have fully deterministic properties, while the SEA subsystems have a high degree of randomness. The method has been recently generalised by allowing the FE components to possess parametric uncertainty, leading to two ensembles of uncertainty: a non-parametric one (SEA subsystems) and a parametric one (FE components). The SEA subsystems ensemble is dealt with analytically, while the effect of the additional FE components ensemble can be dealt with by Monte Carlo Simulations. However, this approach can be computationally intensive when applied to complex engineering systems having many uncertain parameters. Two different strategies are proposed: (i) the combination of the hybrid FE/SEA method with the First Order Reliability Method which allows the probability of the non-parametric ensemble average of a response variable exceeding a barrier to be calculated and (ii) the combination of the hybrid FE/SEA method with Laplace's method which allows the evaluation of the probability of a response variable exceeding a limit value. The proposed approaches are illustrated using two built-up plate systems with uncertain properties and the results are validated against direct integration, Monte Carlo simulations of the FE and of the hybrid FE/SEA models. © 2013 Elsevier Ltd.

MEMS-based mechanical AGC for oscillator circuits

This paper investigates a nonlinear amplitude saturation behavior in an electrostatically transduced, silicon MEMS disk resonator operating in its secondary elliptical bulk-mode (SEBM) at 3.932 MHz towards its implementation as an all-mechanical automatic gain control (AGC) element. The nonlinear vibration behavior of the SEBM mode is experimentally observed in open-loop testing such that above a threshold small signal drive voltage at a given polarization voltage, the vibration amplitude of the SEBM mode saturates. We also study this nonlinearity in an oscillator circuit designed such that the driving power level at the resonator input can be manually tuned as the circuit operates. The measurements of the voltage amplitudes show a clear transition from the linear to the nonlinear saturation region as the driving power is increased. Short-term frequency stability measurements were also conducted for different v ac and the resulting Allan deviation plots show an improvement in the short-term stability from 1.4 ppb in the linear region to 0.4 ppb in the amplitude saturation region. © 2013 IEEE.

Minimalistic models of an energy-efficient vertical-hopping robot

The use of free vibration in elastic structure can lead to energy-efficient robot locomotion, since it significantly reduces the energy expenditure if properly designed and controlled. However, it is not well understood how to harness the dynamics of free vibration for the robot locomotion, because of the complex dynamics originated in discrete events and energy dissipation during locomotion. From this perspective, the goals of this paper are to propose a design strategy of hopping robot based on elastic curved beams and actuated rotating masses and to identify the minimalistic model that can characterize the basic principle of robot locomotion. Since the robot mainly exhibits vertical hopping, three 1-D models are examined that contain different configurations of simple spring-damper-mass components. The real-world and simulation experiments show that one of the models best characterizes the robot hopping, through analyzing the basic kinematics and negative works in actuation. Based on this model, the self-stability of hopping motion under disturbances is investigated, and design and control parameters are analyzed for the energy-efficient hopping. In addition, further analyses show that this robot can achieve the energy-efficient hopping with the variation in payload, and the source of energy dissipation of the robot hopping is investigated. © 1982-2012 IEEE.

Minimalistic models of an energy efficient vertical hopping robot

The use of free vibration in elastic structure can lead to energy efficient robot locomotion, since it significantly reduces the energy expenditure if properly designed and controlled. However, it is not well understood how to harness the dynamics of free vibration for the robot locomotion, because of the complex dynamics originated in discrete events and energy dissipation during locomotion. From this perspective, this paper explores three minimalistic models of free vibration that can characterize the basic principle of robot locomotion. Since the robot mainly exhibits vertical hopping, three one-dimensional models are examined that contain different configurations of simple spring-damper-mass components. The self-stability of these models are also investigated in simulation. The real-world and simulation experiments show that one of the models best characterizes the robot hopping, through analyzing the basic kinematics and negative works in actuation. Based on this model, the control parameters are analyzed for the energy efficient hopping. © 2013 IEEE.